93 research outputs found
Structured Error Recovery for Codeword-Stabilized Quantum Codes
Codeword stabilized (CWS) codes are, in general, non-additive quantum codes
that can correct errors by an exhaustive search of different error patterns,
similar to the way that we decode classical non-linear codes. For an n-qubit
quantum code correcting errors on up to t qubits, this brute-force approach
consecutively tests different errors of weight t or less, and employs a
separate n-qubit measurement in each test. In this paper, we suggest an error
grouping technique that allows to simultaneously test large groups of errors in
a single measurement. This structured error recovery technique exponentially
reduces the number of measurements by about 3^t times. While it still leaves
exponentially many measurements for a generic CWS code, the technique is
equivalent to syndrome-based recovery for the special case of additive CWS
codes.Comment: 13 pages, 9 eps figure
Block synchronization for quantum information
Locating the boundaries of consecutive blocks of quantum information is a
fundamental building block for advanced quantum computation and quantum
communication systems. We develop a coding theoretic method for properly
locating boundaries of quantum information without relying on external
synchronization when block synchronization is lost. The method also protects
qubits from decoherence in a manner similar to conventional quantum
error-correcting codes, seamlessly achieving synchronization recovery and error
correction. A family of quantum codes that are simultaneously synchronizable
and error-correcting is given through this approach.Comment: 7 pages, no figures, final accepted version for publication in
Physical Review
Structured Near-Optimal Channel-Adapted Quantum Error Correction
We present a class of numerical algorithms which adapt a quantum error
correction scheme to a channel model. Given an encoding and a channel model, it
was previously shown that the quantum operation that maximizes the average
entanglement fidelity may be calculated by a semidefinite program (SDP), which
is a convex optimization. While optimal, this recovery operation is
computationally difficult for long codes. Furthermore, the optimal recovery
operation has no structure beyond the completely positive trace preserving
(CPTP) constraint. We derive methods to generate structured channel-adapted
error recovery operations. Specifically, each recovery operation begins with a
projective error syndrome measurement. The algorithms to compute the structured
recovery operations are more scalable than the SDP and yield recovery
operations with an intuitive physical form. Using Lagrange duality, we derive
performance bounds to certify near-optimality.Comment: 18 pages, 13 figures Update: typos corrected in Appendi
Approximate quantum error correction for generalized amplitude damping errors
We present analytic estimates of the performances of various approximate
quantum error correction schemes for the generalized amplitude damping (GAD)
qubit channel. Specifically, we consider both stabilizer and nonadditive
quantum codes. The performance of such error-correcting schemes is quantified
by means of the entanglement fidelity as a function of the damping probability
and the non-zero environmental temperature. The recovery scheme employed
throughout our work applies, in principle, to arbitrary quantum codes and is
the analogue of the perfect Knill-Laflamme recovery scheme adapted to the
approximate quantum error correction framework for the GAD error model. We also
analytically recover and/or clarify some previously known numerical results in
the limiting case of vanishing temperature of the environment, the well-known
traditional amplitude damping channel. In addition, our study suggests that
degenerate stabilizer codes and self-complementary nonadditive codes are
especially suitable for the error correction of the GAD noise model. Finally,
comparing the properly normalized entanglement fidelities of the best
performant stabilizer and nonadditive codes characterized by the same length,
we show that nonadditive codes outperform stabilizer codes not only in terms of
encoded dimension but also in terms of entanglement fidelity.Comment: 44 pages, 8 figures, improved v
Quantum Error Correction via Noise Guessing Decoding
Quantum error correction codes (QECCs) play a central role both in quantum
communications and in quantum computation, given how error-prone quantum
technologies are. Practical quantum error correction codes, such as stabilizer
codes, are generally structured to suit a specific use, and present rigid code
lengths and code rates, limiting their adaptability to changing requirements.
This paper shows that it is possible to both construct and decode QECCs that
can attain the maximum performance of the finite blocklength regime, for any
chosen code length and when the code rate is sufficiently high. A recently
proposed strategy for decoding classical codes called GRAND (guessing random
additive noise decoding) opened doors to decoding classical random linear codes
(RLCs) that perform near the capacity of the finite blocklength regime. By
making use of the noise statistics, GRAND is a noise-centric efficient
universal decoder for classical codes, providing there is a simple code
membership test. These conditions are particularly suitable for quantum systems
and therefore the paper extends these concepts to quantum random linear codes
(QRLCs), which were known to be possible to construct but whose decoding was
not yet feasible. By combining QRLCs and a newly proposed quantum GRAND, this
paper shows that decoding versatile quantum error correction is possible,
allowing for QECCs that are simple to adapt on the fly to changing conditions.
The paper starts by assessing the minimum number of gates in the coding circuit
needed to reach the QRLCs' asymptotic performance, and subsequently proposes a
quantum GRAND algorithm that makes use of quantum noise statistics, not only to
build an adaptive code membership test, but also to efficiently implement
syndrome decoding
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